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Meeting	ACGS Committee Meeting 122 - Savannah, GA - October 2018
Agenda Location	9 SUBCOMMITTEE E – Flight, Propulsion, and Autonomous Vehicle Control Systems 9.3 Homotopy and Parallelization for Footprints for Hypersonic Vehicles
Title	Homotopy and Parallelization for Footprints for Hypersonic Vehicles
Presenter	Mike Bolander
Affiliation	AFRL
Available Downloads*	presentation
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Abstract	To solve optimal control problems for hypervelocity vehicles in a computationally efficient manner, it is common to make assumptions that simplify the problem, such as flight at maximum lift-to-drag ratio or equilibrium glide. Such assumptions are usually taken to reduce the dimensionality of the dynamical system, and may result in analytical expressions for the control that require a numerical search over a small number of parameters instead of solving the full-order optimal control problem. However, these assumptions have been shown to not always result in favorable comparisons with the numerical solution of the “full” optimal control problem. This paper addresses the problem of trajectory optimization by utilizing known integrals-of-motion and an analysis of the behavior of the co-states for a family of trajectories. It is shown that it is possible to simultaneously reduce the dimensionality of the optimal control problem without affecting the underlying physics, and yet also provide a quality initial guess for the co-states. The latter is important for the solution of optimal control problems using indirect methods